Page 327 - Dust Explosions in the Process Industries

296 Dust Explosions in the Process Industries

Here, yu and "/b are the specific heat ratios for the unburned and burned mixture. Nagy
et al. simplified the calculation by assuming an average value for neglecting the dif-
ference between "/u and "/b. The resulting equation (4.57) for (dPIdt),assuming that the
initial conditions Su,,, To,and Po equals the reference conditions S,,, T,, and P,, is sim-
ilar to equation (4.53) but contains yas a complicatingparameter and must be integrated
numerically:

(4.57)

Values of both p and Sa,, can be determinedfrom equation (4.57) and experimentaldata
for P(t),by plotting the experimental(dPIdt)I[1-(Po/P)1/y]2/3as a function of P in a double
logarithmic diagram. Then, p is determined from the slope and Su,ofrom the intercept
with the ordinate axis (log P = 0). This theoretical treatment yielded a reasonable burn-
ing velocity for 7.7 vol% acetylene in air, &, = 1.1 m/s, which is close to values from
direct measurements.
However, when applying this approach to data from corn starch explosions in a 3 m3
rectilinear closed vessel, p was found to be 0.36, which appearsreasonable, but was
found to be 3.15 m/s, which is about 10 times the experimental laminar burning veloc-
ities for corn starch in air. Nagy et al. pointed out that this high apparent value was most
probably due to the turbulent conditionsin the explosion. It is therefore necessary, when
trying to determine laminar burning velocities from closed-bomb dust explosion exper-
iments, to correct for the inevitable initial turbulence in such experiments. Nagy and
Verakis (1983) attempted to do this and derived laminar burning velocities for clouds in
air of various dusts by applying a modified form of equation (4.53) to experimentaldust
explosion data from the elongated 1.2 liter Hartmann bomb. Corrections were made for
the increase in the initial pressure due to the dispersing air. The first modification made
in equation (4.53) was that the ratio 3IR for a spherical vessel was replaced by the gen-
eral ratio AIV for any arbitrary vessel shape, where A is the internal surface area of the
vessel and V is the vessel volume. Second, the initial laminar burning velocity, Su,,, at
atmospheric pressure and 300 K, was replaced by the corresponding turbulent burning
velocity Su,oa,where a is a turbulence enhancement factor, >1. Furthermore, p was
taken as equal to 0. The generalization of the theory to nonspherical vessels was justi-
fied by referring to the work on premixed gases by Ellis (1928) and Ellis and Wheeler
(1928), and later work at the U.S. Bureau of Mines. These investigationsindicated that,
in nonspherical vessels, the initially spherical flame front gradually assumes the vessel
shape.
The modified version of equation (4.53) suggests that a straight line should result if
(dPIdt)is plotted as a function of [1-(Po/P)]2/3(PIP,). The slope of this line determines
the apparent turbulent burning velocity &,a.It was then simply assumed that a=3.0
could be used as a representative average value for all the Hartmann bomb experiments.
The resulting Su,,values are given in Table 4.7. No information on particle size is given
explicitly; therefore, the possibilities of detailed interpretation are limited. The values
are generally on the same order as laminar burning velocities determinedby other meth-
ods, but it is clearly unsatisfactory to have to rely on somewhat arbitrary estimates of
the factor a.